Metropolitan Area is not a political division, is a meausure of the area of the built city and others under its sphere of influence. Maybe Dallas is the largest in a POLITICAL DIVISION, adding the areas of the political divisions (county) where the built area is. Is like measuring the area of a country. And for measuring the metropolitan area of a city the built surface doesn´t need to be continuos for all its stretch. It´s a matter of density and influence. For instance if a central city has other satellite cities with countryside between them, for the metro area you count the contiunous built area of this cities but not the rural area in between. But of course all depends on the criterion used for understanding "continous built area", that can be for example buildings apart between each other more than 200 metres (as I said is a matter of density). And also the definition of Metro Area itself depens on the criterion used. That´s why is important to compare the metro areas with same criterion. In few words, that the same guys look the sat pictures, see the road connections, analyze the census stats, and better if they can be in the metro areas. The most standard study I know is the one of Kenworth and Laube (I study Architecture and several times I´ve used this stats). For them Tokio is the largest metro area in terms of area (and also people), followed near by New York. The problem is that they don´t count the entire metro area of London, which is very low-density and may have a larger urban area.